White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance D from the slits. At a point on a screen directly in front of one of the slits, certain wavelength are missing. Some of these wavelengths are:

(A) $λ=\frac{b^2}{D}$
(B) $λ=\frac{2b^2}{D}$
(C) $λ=\frac{b^2}{3D}$
(D) $λ=\frac{2b^2}{3D}$

Choose the correct answer from the options given below:

(A) and (C) only

The correct answer is Option (4) → (A) and (C) only

Path Difference $(Δx)=\frac{yb}{d}$

Hence, Path difference $(Δx)$ at any point in front of a slit = $\frac{b^2}{2d}$

for some of wavelength to be missing, some of its odd multiple of half its wavelength must be equal to path difference.

$∴\frac{b^2}{2d}=\left(m+\frac{1}{2}\right)λ$

for $m = 0,λ\frac{b^2}{d}$

for $m = 1,λ\frac{b^2}{3d}$